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On the Physical Inadequacy of Singularities and the Unified Frequency-Governed Framework of Extended Classical Mechanics (ECM)

Authors: Thakur, Soumendra Nath;

On the Physical Inadequacy of Singularities and the Unified Frequency-Governed Framework of Extended Classical Mechanics (ECM)

Abstract

The classical black-hole singularity remains one of the most mathematically accepted yet physically unresolved constructs in modern theoretical physics. Within General Relativity (GR), the internal core of a black hole is formally represented by the limiting condition r = 0, implying L = 0, d = 0, and therefore V = 0. This raises a foundational physical contradiction: if a black hole is claimed to obey the relativistic mass-energy relation E = Mc², then the associated mass (M) must remain physically meaningful, which ordinarily requires nonzero spatial support. This paper argues that a strictly zero-dimensional singular core cannot be regarded as a legitimate physical object because it forfeits both spatial existence and localized mass meaning. Once the Planck boundary (ℓ P = √(ℏG/c³)) is recognized as the lower limit of reliable physical interpretation, the singularity must be understood not as a real object, but as a signal of formal breakdown in the classical geometric framework. To address this inadequacy, the paper introduces an alternative interpretation through Extended Classical Mechanics (ECM). In ECM, sub-Planck collapse does not terminate in geometric divergence, but transforms through a deterministic, frequency-governed energetic transition: 1 ΔPE ECM ↔ M app ↔ ΔM M ↔ ΔKE ECM governed by the intrinsic frequency relation: f source = f observed + Δf source Under this framework, the black hole is reinterpreted not as an inaccessible zero-volume paradox, but as a dynamic energetic transformer whose internal frequency evolution continuously maps to its external gravitational footprint. ECM therefore restores physical continuity, preserves spatial interpretability, and offers a conceptually unified alternative to classical singularity-based black-hole ontology.

Keywords

General Relativity, Frequency-Governed Physics, Sub-Planck Physics, Singularity, Gravitational Emergence, ΔKEECM, (4-(m-Chlorophenylcarbamoyloxy)-2-butynyl)trimethylammonium Chloride, Schwarzschild Solution, Black Hole, Planck Length, Mapp, Spatial Admissibility, ΔKEᴇᴄᴍ, Energetic Manifestation, ΔPEᴇᴄᴍ, Mᵃᵖᵖ, ΔPEECM, ΔMᴍ, ΔMM, Extended Classical Mechanics (ECM), Physical Observability, Gravitational Emergence;

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green